Sparse high-degree polynomials for wide-angle lenses

Rendering with accurate camera models greatly increases realism and improves the match of synthetic imagery to real-life footage. Photographic lenses can be simulated by ray tracing, but the performance depends on the complexity of the lens system, and some operations required for modern algorithms, such as deterministic connections, can be difficult to achieve. We generalise the approach of polynomial optics, i.e. expressing the light field transformation from the sensor to the outer pupil using a polynomial, to work with extreme wide angle (fisheye) lenses and aspherical elements. We also show how sparse polynomials can be constructed from the large space of high-degree terms (we tested up to degree 15). We achieve this using a variant of orthogonal matching pursuit instead of a Taylor series when computing the polynomials. We show two applications: photorealistic rendering using Monte Carlo methods, where we introduce a new aperture sampling technique that is suitable for light tracing, and an interactive preview method suitable for rendering with deep images.